Certain applications require precise determination of the differences in piston and tilt that exist between respective wavefronts of several light beams.
Such a need appears in particular during the adjustment of a mirror of a telescope of the Keck type. Such a mirror is constituted by a juxtaposition of separate mirror segments, each most frequently having a hexagonal peripheral limit. It is thus possible to form a complete mirror of approximately ten meters in diameter, with segments that individually measure approximately one meter in diameter. However, the mirror segments must be adjusted for height and inclination with respect to one another so that the wavefront of a light beam that is reflected by the complete mirror does not have steps or sudden variations in slope, which would be caused by differences in height and inclination present between neighbouring mirror segments.
The need also appears when the light beams from various laser sources are combined coherently in order to obtain a resulting high-intensity beam. The number of individual laser sources can be considerable when the light intensity desired in the combination beam is very high. In the case of monochromatic laser sources, the individual wavefronts of the beams which originate respectively from the laser sources, and which correspond to one and the same phase value, must be combined without phase errors. The thesis by B Toulon, defended on 20 Nov. 2009 at Université Paris XI Orsay and entitled “La mesure d'amplitudes complexes par interférométrie à décalage multi-latéral” [Measurement of complex amplitudes by multilateral shearing interferometry] proposes in particular a method based on quadrilateral shearing interferometry, for measuring differences in piston and tilt between 64 laser sources. In the case of pulsed laser sources, the combination of the individual pulses that are produced respectively by the laser sources, is not itself a pulse the duration of which is similar to that of the individual pulses, unless no significant delay exists for certain of the individual pulses with respect to others, and no differences between their directions of propagation. For these applications of coherent combination of monochromatic light beams or light pulses, a wavefront sensor based on interference is used, which comprises:                an optical input, intended to receive a light radiation having an initial wavefront that extends through said optical input;        a radiation splitter, arranged in order to produce, from light beams that originate respectively from restricted zones within the optical input, several sub-beams for each light beam, each sub-beam reproducing characteristics of the initial wavefront existing in the corresponding restricted zone;        optical paths, arranged in order to superimpose sub-beams that originate respectively from different restricted zones within the optical input, and which each pass via a different optical path;        at least one image detector, arranged in order to capture interference patterns that are produced by the superimposed sub-beams; and        a processing module, suitable for determining, from the interference patterns, differences in piston and tilt that exist for the initial wavefront between the restricted zones from which the superimposed sub-beams originate.        
The wavefront sensor is then used in order to characterize the overall wavefront that results from the individual wavefronts, produced separately by the laser sources.
In the device mentioned by B. Toulon, the radiation splitter is a diffraction grating that produces four replicas of the initial wavefront, corresponding to the combinations of two orders of diffraction, each equal to +1 or −1. The radiation splitter thus produces four sub-beams from each light beam. The restricted zones within the optical input correspond to the sections of the individual light beams that originate from the juxtaposed laser sources. These are equipped with output microlenses, so that the individual beams each have a parallel, or collimated, beam structure. The image detector then captures a combination of four-beam interferograms, from which the differences in piston and tilt that exist between two laser sources that are neighbouring within the optical input can be determined. Depending on the orientation of the diffraction grating with respect to the squared pattern of the distribution of the laser sources in the optical input, two different interference modes are obtained. But in these two modes, the interferograms all have a complex structure, with overlapping zones of different categories. For this reason, the determination of differences in piston and tilt from any one of the interferograms is a difficult task.
The article by C. Bellanger et al., entitled “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining”, Optics Letters, 1 Dec. 2010, vol. 35, No. 23, pp 3931-3933, relates to a quadriwave lateral shearing interferometer of the same type.